Task 3 The Euclidean distance between any two points P and Q is given by: Distance PQ√√√(x1 − x2)² + (y1 — Y2)² = And the area of a triangle given its three vertices A, B and Ccan be calculated using Heron's formula: a b Figure 3 C a+b+c S 2 Area √s(sa)(s - b)(s - c) = where a, b and c are the lengths of the sides of the triangle. Write a script that prompts the user to enter the coordinates of three points that form a triangle. The script should calculate the area of the triangle. It will call one function to calculate the area of the triangle using Heron's formula. This function will call subfunctions to calculate the length of each side using the Euclidean distance formula. Additionally, ensure the script verifies if the points form a valid triangle. If they do not (i.e., when the calculated area is zero), the script should display a clear and sensible error message indicating the invalidity of the triangle.

C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter13: Structures
Section: Chapter Questions
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Task 3
The Euclidean distance between any two points P and Q is given by:
Distance PQ√√√(x1 − x2)² + (y1 — Y2)²
=
And the area of a triangle given its three vertices A, B and Ccan be calculated using Heron's
formula:
a
b
Figure 3
C
a+b+c
S
2
Area √s(sa)(s - b)(s - c)
=
where a, b and c are the lengths of the sides of the triangle.
Write a script that prompts the user to enter the coordinates of three points that form a
triangle. The script should calculate the area of the triangle. It will call one function to calculate
the area of the triangle using Heron's formula. This function will call subfunctions to calculate
the length of each side using the Euclidean distance formula.
Additionally, ensure the script verifies if the points form a valid triangle. If they do not (i.e.,
when the calculated area is zero), the script should display a clear and sensible error message
indicating the invalidity of the triangle.
Transcribed Image Text:Task 3 The Euclidean distance between any two points P and Q is given by: Distance PQ√√√(x1 − x2)² + (y1 — Y2)² = And the area of a triangle given its three vertices A, B and Ccan be calculated using Heron's formula: a b Figure 3 C a+b+c S 2 Area √s(sa)(s - b)(s - c) = where a, b and c are the lengths of the sides of the triangle. Write a script that prompts the user to enter the coordinates of three points that form a triangle. The script should calculate the area of the triangle. It will call one function to calculate the area of the triangle using Heron's formula. This function will call subfunctions to calculate the length of each side using the Euclidean distance formula. Additionally, ensure the script verifies if the points form a valid triangle. If they do not (i.e., when the calculated area is zero), the script should display a clear and sensible error message indicating the invalidity of the triangle.
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